Inflation regimes, core inflation measures and the relationship between producer and consumer price inflation

Abstract

To date, an overwhelming majority of the literature has addressed mean relationships between producer and consumer price inflation. Granger et al . (1986) represent the only attempt to investigate second moment relationships. We examine the consumer--producer price relationship employing a multivariate GARCH-M framework that allows simultaneous estimation of the bivariate system along with providing explicit times series estimates of the variances of consumer and producer price inflation. This research also breaks new ground in the use of core and over-all inflation variance measures as well as examining state dependent mean and variance relationships. We find that mean relationships are generally sensitive to the measure of inflation used. Food and energy prices play an important role in transmitting changes in aggregate input prices to aggregate output prices. When food and energy prices are eliminated from consumer and producer price inflation measures, mean relationships break down irrespective of whether the economy is experiencing a high or low inflation regime. Variance relationships appear to be more robust in general and input price relationships in particular appear to respond to inflation regime shifts.

Notes

¹ See Pokins (1974), Guthrie (1981), Cushing and McGarvey (1990), Engle (1978) and Silver and Wallace (1980).

² See Gordon (1975), Engle et al . (1982) and Tiffin and Dawson (2000).

³ Granger et al . (1986) explicitly argue that the estimation methodology that they employ is inadequate to properly estimate a complete bivariate system.

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⁶ Garner (1995) uses the percent change in CPI inflation from 12 months earlier over the period 1960 to 1995 to get the series used in predicting inflation turning points. The precise months for troughs as defined by Garner (1995) are: November 1961, August 1972, December 1976 and December 1986. For peaks: February 1970, November 1974, April 1980 and October 1990. The turning points that occurred before 1960 were estimated by the author using Garner's methodology.

⁷ Both the test for ARCH effects and the Ljung--Box test use the χ² distribution to evaluate test statistics, therefore we provide the critical values at the 0.05 level of significance for lags = 2, 4, 8, 12, 24 and 36. They are 5.99, 9.49, 15.51, 21.03, 36.42 and 50.71.

⁸ Squared conditional means for all four variables are estimated using Equations 26–29. A one-step-ahead forecast is developed for each variable across successive periods of the data set. The forecast are squared and a 12 period weighted average as in footnotes 3 and 4 are calculated for each variable.

⁹ In earlier drafts of this article we followed Granger et al . (1986) and placed squared levels of input price inflation in the variance equation of consumer price inflation. In all case the variable was nonsignificant and was not used in the models reported in this article.

¹⁰ In earlier drafts of this paper we followed Granger et al . (1986) and placed squared levels of output price inflation in the variance equation of producer price inflation. In all case the variable was nonsignificant and was not used in the models reported in this article.

¹¹ Bollerslev (1986) developed the constant correlation model. Several other covariance models were examined; however, the basic conclusions of this article were unaffected.